def rod_setup(dim1: Tuple[float], dim2: Tuple[float]) -> Faces: # validated
"""defines points in a circle with triangle based end caps"""
# 4,8,12,16,... becomes 5,9,13,17,...
ntheta = 17
thetas = np.radians(np.linspace(0., 360., ntheta))
nfaces = 0
all_faces = []
points_list = []
x = np.zeros(ntheta)
for dim in (dim1, dim2):
radius, = dim
y = radius * np.cos(thetas)
z = radius * np.sin(thetas)
xyz = np.vstack([x, y, z]).T
assert xyz.shape == (ntheta, 3), xyz.shape
# the tri_cap buils triangles that fan out from the first node
tris = tri_cap(ntheta)
# we need to use the tolist because we're going to
# combine quads and tris (the elements have different
# lengths)
all_faces += (nfaces + tris).tolist()
nfaces += tris.shape[0]
points_list.append(xyz)
# the main cylinder uses the points defined independent
# of the points n1/n2
faces = elements_from_quad(2, ntheta)
all_faces += faces.tolist()
return all_faces, points_list[0], points_list[1]
def tube_faces(n1: int, n2: int, xform, dim1: Tuple[float, float],
dim2: Tuple[float, float]): # validated
"""
defines a rod with a hole
"""
# 4,8,12,16,... becomes 5,9,13,17,...
thetas = np.radians(np.linspace(0., 360., 17))
ntheta = len(thetas)
npoints = ntheta * 2
points_list1 = []
points_list2 = []
x = np.zeros(ntheta)
for nid, dim in [(n1, dim1), (n2, dim2)]:
radius_out, radius_in = dim
# outer rod
y = radius_out * np.cos(thetas)
z = radius_out * np.sin(thetas)
xyz1 = np.vstack([x, y, z]).T
points1i = xyz1 @ xform + nid
points_list2.append(points1i)
# inner rod
y = radius_in * np.cos(thetas)
z = radius_in * np.sin(thetas)
xyz2 = np.vstack([x, y, z]).T
points2i = xyz2 @ xform + nid
points_list1.append(points2i)
# the main cylinder uses the points defined independent
# of the inner/outer faces
faces_n1 = elements_from_quad(2, ntheta)
faces_n2 = faces_n1 + npoints
#faces_n1
#[[ 0 17 18 1]
#[ 1 18 19 2]
#[ 2 19 20 3]
#[ 3 20 21 4]
#[ 4 21 22 5]
#[ 5 22 23 6]
# we use slicing to link the outer surface to the
# inner surface using quads
#
# we'd like to hstack the column arrays, but hstack and a
# transpose is easier. Presumably, a "newaxis" index would work...
faces_out = np.vstack(
[faces_n1[:, 0], faces_n1[:, 3], faces_n2[:, 3], faces_n2[:, 0]]).T
faces_in = np.vstack(
[faces_n1[:, 1], faces_n1[:, 2], faces_n2[:, 2], faces_n2[:, 1]]).T
# combine everything together
all_faces = np.vstack([faces_n1, faces_n2, faces_out, faces_in])
points = np.vstack(points_list1 + points_list2)
return all_faces, points, points.shape[0]
def tube_setup(
dim1: Tuple[float, float], dim2: Tuple[float, float]
) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: # validated
"""defines a rod with a hole"""
# 4,8,12,16,... becomes 5,9,13,17,...
ntheta = 17
thetas = np.radians(np.linspace(0., 360., ntheta))
npoints = ntheta * 2
x = np.zeros(ntheta)
points = []
#points_list_in = []
#points_list_out = []
for dim in (dim1, dim2):
radius_out, radius_in = dim
# inner rod
y = radius_in * np.cos(thetas)
z = radius_in * np.sin(thetas)
xyz2 = np.vstack([x, y, z]).T
#points_list_in.append(xyz2)
# outer rod
y = radius_out * np.cos(thetas)
z = radius_out * np.sin(thetas)
xyz1 = np.vstack([x, y, z]).T
#points_list_out.append(xyz1)
xyz = np.vstack([xyz1, xyz2])
points.append(xyz)
# the main cylinder uses the points defined independent
# of the inner/outer faces
faces_n1 = elements_from_quad(2, ntheta)
faces_n2 = faces_n1 + npoints
#faces_n1
#[[ 0 17 18 1]
#[ 1 18 19 2]
#[ 2 19 20 3]
#[ 3 20 21 4]
#[ 4 21 22 5]
#[ 5 22 23 6]
# we use slicing to link the outer surface to the
# inner surface using quads
#
# we'd like to hstack the column arrays, but hstack and a
# transpose is easier. Presumably, a "newaxis" index would work...
faces_out = np.vstack(
[faces_n1[:, 0], faces_n1[:, 3], faces_n2[:, 3], faces_n2[:, 0]]).T
faces_in = np.vstack(
[faces_n1[:, 1], faces_n1[:, 2], faces_n2[:, 2], faces_n2[:, 1]]).T
# combine everything together
all_faces = np.vstack([faces_n1, faces_n2, faces_out, faces_in])
return all_faces, points[0], points[1]
def rod_faces(n1: int, n2: int, xform, dim1: Tuple[float, float],
dim2: Tuple[float, float]): # validated
"""
defines points in a circle with triangle based end caps
"""
# 4,8,12,16,... becomes 5,9,13,17,...
thetas = np.radians(np.linspace(0., 360., 17))
ntheta = len(thetas)
nfaces = 0
all_faces = []
points_list = []
x = np.zeros(ntheta)
for nid, dim in [(n1, dim1), (n2, dim2)]:
radius, = dim
y = radius * np.cos(thetas)
z = radius * np.sin(thetas)
xyz = np.vstack([x, y, z]).T
assert xyz.shape == (ntheta, 3), xyz.shape
pointsi = xyz @ xform + nid
points_list.append(pointsi)
# the tri_cap is made from points that aren't defined yet
# (the n1/n2 end points)
tris = tri_cap(ntheta)
# we need to use the tolist because we're going to
# combine quads and tris (the elements have different
# lengths)
all_faces += (nfaces + tris).tolist()
nfaces += tris.shape[0]
# the main cylinder uses the points defined independent
# of the points n1/n2
faces = elements_from_quad(2, ntheta)
all_faces += faces.tolist()
# used by the tri_caps
points_list.append(n1)
points_list.append(n2)
points = np.vstack(points_list)
return all_faces, points, points.shape[0]